Question

Using Cramer's Rule, what is the value of x in the solution to the system of linear equations below?
5x-4 = 3y
2x+32 = 4y
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WIN
Ô CO

Answer 1

Answer:

The value of X in the solution to the system of linear equations below

5x-4=3y

2x+32= 4y  is  8.

Step-by-step explanation:

Solution:

First write the expression in the form of ax by = c

Therefore the equations are as

$5x-3y=4\ and\\2x-4y=-32$

Now we will write in linear equation in matrix form

$\left[\begin{array}{cc}5&-3\\2&-4\end{array}{}\right] \left[\begin{array}{c}x\\y\end{array}{}\right]= \left[\begin{array}{c}4\\-32\end{array}{}\right]$

By Cramer's rule we have

$x = \frac{Dx}{D}$

Where D is the determinant of 2 x 2 matrix

and Dx is the determinant after replacing the x coefficient by the constants

$Det\left[\begin{array}{cc}5&-3\\2&-4\end{array}{}\right]= 5\times-4-(-3\times2)\\\\=-20+6\\\therefore D= -14$

For Dx  we will have

$Dx= \left[\begin{array}{cc}4&-3\\-32&-4\end{array}{}\right]= 4\times-4-(-3\times -32)\\\\=-16-96\\= -112\\\therefore Dx = -112$

Now by Cramer's rule

$x = \frac{Dx}{D}\\= \frac{-112}{-14}\\= 8\\ \therefore x = 8$

Answer 2

Answer:

ANSWER IS C

Step-by-step explanation:

EDGE 2021